Rectified 6-orthoplex

Rectified 6-orthoplex
(OFF file)
Rank	6
Type	Uniform
Notation
Bowers style acronym	Rag
Coxeter diagram	o4o3o3o3x3o ()
Elements
Peta	12 5-orthoplexes, 64 rectified 5-simplices
Tera	384 pentachora, 192 rectified pentachora
Cells	960 tetrahedra, 240 octahedra
Faces	160+960 triangles
Edges	480
Vertices	60
Vertex figure	Hexadecachoric prism, edge length 1
Measures (edge length 1)
Circumradius	1
Hypervolume	${\frac {29}{45}}\approx 0.64444$
Dipetal angles	Rix–rap–rix: $\arccos \left(-{\frac {2}{3}}\right)\approx 131.81032^{\circ }$
	Tac–pen–rix: $\arccos \left(-{\frac {\sqrt {6}}{6}}\right)\approx 114.09484^{\circ }$
Central density	1
Number of external pieces	76
Level of complexity	5
Related polytopes
Army	Rag
Regiment	Rag
Conjugate	None
Abstract & topological properties
Flag count	230400
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B6, order 46080
Convex	Yes
Nature	Tame

The rectified 6-orthoplex, or rag, also called the rectified hexacontatetrapeton, is a convex uniform 6-polytope. It consists of 12 regular 5-orthoplexes and 64 rectified 5-simplices. Two 5-orthoplexes and 16 rectified 5-simplices join at each hexadecachoric prismatic vertex. As the name suggests, it is the rectification of the 6-orthoplex.

The rectified 6-orthoplex contains the vertices of a square-hexadecachoric duoprism and octahedral duoprism.

Vertex coordinates

The vertices of a rectified 6-orthoplex of edge length 1 are given by all permutations of:

• $\left(\pm {\frac {\sqrt {2}}{2}},\,\pm {\frac {\sqrt {2}}{2}},\,0,\,0,\,0,\,0\right)$.

Representations

A rectified 6-orthoplex has the following Coxeter diagrams:

• o4o3o3o3x3o () (full symmetry)
• o3o3o3x3o *b3o () (D₆ symmetry)
• ooo4ooo3ooo3oxo3xox&#xt (B₅ axial, triacontaditeron-first)
• ooo3ooo3ooo *b3oxo3xox&#xt (D₅ symmetry, as above with half symmetry)
• oxo3xoo3ooo3oox3oxo&#xt (A₅ axial, rectified hexateron-first)
• ooo4oox3oxo ooo4xoo3oxo&#zx (B₃×B₃ symmetry)

Gallery

• 

  B₅ orthographic projection

• 

  B₄

• 

  B₃

• 

  B₂

• 

  A₅

• 

  A₃

Related polytopes

The rectified 6-orthoplex is the colonel of a regiment that includes a total of 132 uniform members, plus five fissaries and two compounds. Of these, 39 of the true members have full symmetry, as do four of the fissaries and both compounds. The remaining uniforms along with one fissary have half symmetry only.

External links

• Klitzing, Richard. "rag".
• Wikipedia contributors. "Rectified 6-orthoplex".